2018年高教社杯全国大学生数学建模竞赛题目 A题

2018年高教社杯全国大学生数学建模竞赛题目

（请先阅读“全国大学生数学建模竞赛论文格式规范”）

A题高温作业专用服装设计

在高温环境下工作时，人们需要穿着专用服装以避免灼伤。专用服装通常由

三层织物材料构成，记为I、II、in层，其中I层与外界环境接触，in层与皮肤

之间还存在空隙，将此空隙记为IV层。

为设计专用服装，将体内温度控制在37℃的假人放置在实验室的高温环境

中，测量假人皮肤外侧的温度。为了降低研发成本、缩短研发周期，请你们利用

数学模型来确定假人皮肤外侧的温度变化情况，并解决以下问题：

（1）专用服装材料的某些参数值由附件1给出，对环境温度为75P、11层厚

度为6mm、IV层厚度为5mm、工作时间为90分钟的情形开展实验，测量得到

假人皮肤外侧的温度（见附件2）o建立数学模型，计算温度分布，并生成温度

分布的Excel文件（文件名为probleml.xlsx）。

（2）当环境温度为65。（3、IV层的厚度为5.5mm时，确定n层的最优厚度,

确保工作60分钟时，假人皮肤外侧温度不超过47。。且超过44P的时间不超

过5分钟。

（3）当环境温度为8（）'C时，确定II层和IV层的最优厚度，确保工作30分

钟时，假人皮肤外侧温度不超过47。（2,且超过44。（2的时间不超过5分钟。

附件1.专用服装材料的参数值

附件2.假人皮肤外侧的测量温度

附件1.专用服装材料的参数值

密度比热热传导率厚度

分层

(kg/nf)(J/(kg*℃))(W/(m•℃))(nun)

I层30013770.0820.6

口层86221000.370.6-25

III层74.217260.0453.6

IV层1.1810050.0280.6-6.4

附件2.假人皮肤外侧的测量温度

时间(s)温度(©

037.00

137.0C

237.0C

337.0C

437.0C

537.0C

637.0C

737.0C

837.0C

937.0C

1037.0C

1137.0C

1237.0C

1337.0C

1437.0C

1537.0C

1637.01

1737.01

1837.01

1937.01

2037.02

2137.02

2237.03

2337.03

2437.04

2537.05

2637.06

2737.07

2837.08

2937.09

3037.1C

3137.12

3237.13

3337.15

3437.ie

3537.18

3637.2C

3737.22

3837.24

3937.26

4037.28

4137.31

4237.33

4337.36

4437.38

4537.41

4637.44

4737.46

4837.49

4937.52

5037.55

5137.58

5237.61

5337.65

5437.68

5537.71

5637.74

5737.78

5837.81

5937.85

6037.88

6137.91

6237.95

6337.99

6438.02

6538.06

6638.09

6738.13

6838.17

6938.20

7038.24

7138.28

7238.32

7338.35

7438.39

7538.43

7638.47

7738.50

7838.54

7938.58

8038.62

8138.65

8238.69

8338.73

8438.77

8538.81

8638.84

8738.88

8838.92

8938.96

9038.99

9139.03

9239.07

9339.11

9439.14

9539.18

9639.22

9739.26

9839.29

9939.33

10039.37

10139.40

10239.44

10339.48

10439.52

10539.55

10639.59

10739.62

10839.66

10939.70

11039.73

11139.77

11239.8C

11339.84

11439.87

11539.91

11639.95

11739.98

11840.02

11940.05

12040.09

12140.12

12240.15

12340.19

12440.22

12540.26

12640.29

12740.32

12840.36

12940.39

13040.43

13140.46

13240.49

13340.52

13440.56

13540.59

13640.62

13740.66

13840.69

13940.72

14040.75

14140.78

14240.82

14340.85

14440.88

14540.91

14640.94

14740.97

14841.0C

14941.03

15041.07

15141.10

15241.13

15341.16

15441.19

15541.22

15641.25

15741.28

15841.31

15941.34

16041.37

16141.4G

16241.42

16341.45

16441.48

16541.51

16641.54

16741.57

16841.60

16941.63

17041.65

17141.68

17241.71

17341.74

17441.77

17541.79

17641.82

17741.85

17841.88

17941.9C

18041.93

18141.96

18241.98

18342.01

18442.04

18542.oe

18642.09

18742.12

18842.14

18942.17

19042.19

19142.22

19242.25

19342.27

19442.30

19542.32

19642.35

19742.37

19842.40

19942.42

20042.45

20142.47

20242.50

20342.52

20442.54

20542.57

20642.59

20742.62

20842.64

20942.67

21042.69

21142.71

21242.74

21342.76

21442.78

21542.81

21642.83

21742.85

21842.87

21942.9C

22042.92

22142.94

22242.97

22342.99

22443.01

22543.03

22643.05

22743.08

22843.10

22943.12

23043.14

23143.16

23243.19

23343.21

23443.23

23543.25

23643.27

23743.29

23843.31

23943.33

24043.35

24143.37

24243.40

24343.42

24443.44

24543.46

24643.48

24743.50

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24943.54

25043.56

25143.58

25243.60

25343.62

25443.64

25543.66

25643.67

25743.69

25843.71

25943.73

26043.75

26143.77

26243.79

26343.81

26443.83

26543.85

26643.86

26743.88

26843.9C

26943.92

27043.94

27143.96

27243.97

27343.99

27444.01

27544.03

27644.05

27744.06

27844.08

27944.10

28044.12

28144.13

28244.15

28344.17

28444.18

28544.2C

28644.22

28744.24

28844.25

28944.27

29044.29

29144.30

29244.32

29344.34

29444.35

29544.37

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30044.45

30144.46

30244.48

30344.50

30444.51

30544.53

30644.54

30744.56

30844.57

30944.59

31044.61

31144.62

31244.64

31344.65

31444.67

31544.68

31644.70

31744.71

31844.73

31944.74

32044.75

32144.77

32244.78

32344.8G

32444.81

32544.83

32644.84

32744.86

32844.87

32944.88

33044.90

33144.91

33244.93

33344.94

33444.95

33544.97

33644.98

33744.99

33845.01

33945.02

34045.03

34145.05

34245.06

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37245.43

37345.45

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38045.53

38145.54

38245.55

38345.56

38445.57

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38945.62

39045.64

39145.65

39245.66

39345.67

39445.68

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39745.71

39845.72

39945.73

40045.74

40145.75

40245.76

40345.77

40445.78

40545.79

40645.8C

40745.81

40845.82

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41045.84

41145.85

41245.86

41345.87

41445.88

41545.89

41645.90

41745.91

41845.92

41945.93

42045.94

42145.95

42245.96

42345.97

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42545.98

42645.99

42746.0C

42846.01

42946.02

43046.03

43146.04

43246.05

43346.06

43446.07

43546.07

43646.08

43746.09

43846.10

43946.11

44046.12

44146.13

44246.13

44346.14

44446.15

44546.16

44646.17

44746.18

44846.19

44946.19

45046.2G

45146.21

45246.22

45346.23

45446.23

45546.24

45646.25

45746.26

45846.27

45946.27

46046.28

46146.29

46246.30

46346.31

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46846.35

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47146.37

47246.38

47346.38

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47746.41

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50346.59

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51946.69

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52146.71

52246.71

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52846.75

52946.75

53046.76

53146.77

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53546.79

53646.79

53746.8C

53846.81

53946.81

54046.82

54146.82

54246.83

54346.83

54446.84

54546.84

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54746.85

54846.86

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55046.87

55146.88

55246.88

55346.89

55446.89

55546.9C

55646.9C

55746.91

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56146.93

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57146.98

57246.98

57346.99

57446.99

57547.0C

57647.00

57747.01

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58047.02

58147.03

58247.03

58347.03

58447.04

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58647.05

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62247.2G

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70647.47

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72147.51

72247.51

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73647.55

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75247.58

75347.59

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75547.59

75647.59

75747.6C

75847.60

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76047.60

76147.6G

76247.61

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77247.63

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87347.79

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87747.80

87847.8C

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88147.8C

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97247.89

97347.9C

97447.9C

97547.90

97647.9C

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98147.90

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102447.93

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